Correlation functions of charged free boson and fermion systems

DOI10.1088/1742-5468/ABA0AAzbMATH Open1459.81056arXiv1912.03870OpenAlexW3104861199MaRDI QIDQ5856865

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Publication date: 30 March 2021

Published in: (Search for Journal in Brave)

Abstract: Using the idea of the quantum inverse scattering method, we introduce the operators

m a t h b f B (x), m a t h b f C (x)

and

m a t h b f i l d e B (x), m a t h b f i l d e C (x)

corresponding to the off-diagonal entries of the monodromy matrix

T

for the phase model and

i

-boson model in terms of bc fermions and neutral fermions respectively, thus giving alternative treatment of the KP and BKP hierarchies. We also introduce analogous operators

m a t h b f B^{*} (x)

and

m a t h b f C^{*} (x)

for the charged free boson system and show that they are in complete analogy to those of

b c

fermionic fields. It is proved that the correlation function

l a n g l e 0 | m a t h b f C (x_{N}) c d o t s m a t h b f C (x_{1}) m a t h b f B (y_{1}) c d o t s

m a t h b f B (y_{N}) | 0 a n g l e

in the

b c

fermionic fields is the inverse of the correlation function

l a n g l e 0 | m a t h b f C^{*} (x_{N}) c d o t s m a t h b f C^{*} (x_{1}) m a t h b f B^{*} (y_{1}) c d o t s m a t h b f B^{*} (y_{N}) | 0 a n g l e

in the charged free bosons.

Full work available at URL: https://arxiv.org/abs/1912.03870

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